4 Leyla investigates the number of shoppers who visit a shop between 10.30 am and 11 am on Saturday mornings. She makes the following assumptions.
- Shoppers visit the shop independently of one another.
- The average rate at which shoppers visit the shop between these times is constant.
- State an appropriate distribution with which Leyla could model the number of shoppers who visit the shop between these times.
Leyla uses this distribution, with mean 14, as her model.
Calculate the probability that, between 10.35 am and 10.50 am on a randomly chosen Saturday, at least 10 shoppers visit the shop.
Leyla chooses 25 Saturdays at random.Find the expected number of Saturdays, out of 25, on which there are no visitors to the shop between 10.35 am and 10.50 am .In fact on 5 of these Saturdays there were no visitors to the shop between 10.35 am and 10.50 am . Use this fact to comment briefly on the validity of the model that Leyla has used.